In short sales, homes are sold for less than what is owed and the bank forgives the excess debt. Banks have been reluctant to approve such deals in the past -- since they take a loss on the home -- but in certain cases, it's become a much better proposition than letting the homeowner fall into foreclosure.

This new approach by the banks has startled plenty of homeowners, according to Elizabeth Weintraub, a Sacramento-area real estate agent who specializes in short sales.

"Initially, the homeowners are skeptical," she said. "The bank may have already turned down their request for a modification. Then, one day, they call and say, 'Let us give you some cash.'"

When Chase Mortgage (JPM, Fortune 500) told Angelique Pierce, that she would receive a check for $25,000 if she sold her house, she couldn't believe it.

"I got the offer in the mail," said the Rancho Cordova, Calif. resident. "I called my bank to ask if it was real."

After Pierce became disabled a few years ago and had to stop working work, she fell behind on payments on both her first and second mortgages, valued at $250,000 and $50,000, respectively.

Now, she's trying to sell her three-bedroom ranch for just $95,000 -- almost half of the $179,000 she paid for the place in late 2002.

From the bank's point of view, the offers make sense, according to Tom Kelly, a spokesman for Chase Mortgage, who would not comment on Pierce or other individual cases. "The first choice is a modification but if that's impossible than a short sale is a faster, more efficient solution," he said.

For the banks, foreclosure has become an increasingly difficult and expensive option. Homeowners have learned to fight the banks tooth and nail, dragging out cases for years.

And as the cases drag, expenses grow. Homeowners not only stop paying their mortgages but they stop paying property taxes and conducting normal maintenance as well. Roofs, siding, plumbing and other parts of the home deteriorate and the property loses value. By the time banks take possession, they're out tens of thousands of dollars.

"I've seen a lot of foreclosures for sale where it would cost a lot more than $20,000 to get them into condition to sell again," said John Hayton, a short sale specialist in Orlando, Fla, who has had a number of clients receive offers from the banks.

Short sales also command higher prices than foreclosed homes. In December, foreclosed properties sold for an average of 22% less than conventional sales, while the discount for short sales was only 14%, according to the National Association of Realtors.

All that has been true for years, but it is only lately that these outsized incentives, which Bloomberg recently reported on, have surfaced.

Sellers are more cooperative when they're going to receive a five-figure check for their troubles.

Nick Chaconas, an agent with discount broker Redfin, wondered why one seller was so anxious to sell their home. "Since I represent the buyer, I didn't even know about the incentive until the closing," he said.

It turned out that the seller's bank was writing her a check for $30,000.

Whether sellers can expect incentives fromtheir banks depends on multiple factors, including where they live.

Wells Fargo (WFC, Fortune 500) limits its offers to certain states, such as Florida, where the foreclosure process can be lengthy, according to spokeswoman Veronica Clemons. The bank haspaid $10,000 to $20,000 to borrowers who short sell or transfer their title to Wells via a deed-in-lieu.

Bank of America (BAC, Fortune 500) had a pilot program in Florida that paid incentives of $5,000 to $20,000 for sales that were initiated between Sept. 26, 2011 and Nov. 30, 2011 and close by the end of this August. The amount of the incentive is based on 5% of the unpaid balance, with a $5,000 minimum and $20,000 maximum.

Jumana Bauwens, Bank of America's spokeswoman, called it a "test-and-run program" that may beexpanded to other states.

The offers are not always a panacea for homeowners struggling to pay the bills, however.

Pierce, for example, has not been able to make hers pay off. She had a buyer but her second mortgage holder refused to go along with the deal unless it got a share of the $25,000 she was being offered by the bank. She said that the bank balked at the deal and the sale was cancelled.

She's looking for another buyer, but it's up in the air if Chase will honor its original offer if the second mortgage holder won't cooperate.